### 111.5.5 Cohomology

Papers discussing cohomology of sheaves on algebraic stacks.

Olsson:

*Sheaves on Artin stacks*[olsson_sheaves]This paper develops the theory of quasi-coherent and constructible sheaves proving basic cohomological properties. This paper corrects a mistake in [LM-B] in the functoriality of the lisse-étale site. The cotangent complex is constructed. In addition, the following theorems are proved: Grothendieck's Fundamental Theorem for proper morphisms, Grothendieck's Existence Theorem, Zariski's Connectedness Theorem and finiteness theorem for proper pushforwards of coherent and constructible sheaves.

Behrend:

*Derived $l$-adic categories for algebraic stacks*[behrend_derived]Proves the Lefschetz trace formula for algebraic stacks.

Behrend:

*Cohomology of stacks*[behrend_cohomology]Defines the de Rham cohomology for differentiable stacks and singular cohomology for topological stacks.

Faltings:

*Finiteness of coherent cohomology for proper fppf stacks*[faltings_finiteness]Proves coherence for direct images of coherent sheaves for proper morphisms.

Abramovich, Corti, Vistoli:

*Twisted bundles and admissible covers*[acv]The appendix contains the proper base change theorem for étale cohomology for tame Deligne-Mumford stacks.

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